脑网络的 Hodge Laplacian。
Hodge Laplacian of Brain Networks.
出版信息
IEEE Trans Med Imaging. 2023 May;42(5):1563-1573. doi: 10.1109/TMI.2022.3233876. Epub 2023 May 2.
Abstract
The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification and modeling of cycles using persistent homology and the Hodge Laplacian. Various statistical inference procedures on cycles are developed. We validate the our methods on simulations and apply to brain networks obtained through the resting state functional magnetic resonance imaging. The computer codes for the Hodge Laplacian are given in https://github.com/laplcebeltrami/hodge.
摘要
大脑网络中的闭环或循环嵌入了更高阶的信号传输路径，为理解大脑的功能提供了基本的认识。在这项工作中，我们提出了一种使用持久同调与赫尔德拉普拉斯算子来系统地识别和建模循环的有效算法。我们还开发了各种关于循环的统计推断程序。我们在模拟中验证了我们的方法，并将其应用于通过静息态功能磁共振成像获得的大脑网络。赫尔德拉普拉斯算子的计算机代码可在 https://github.com/laplcebeltrami/hodge 获得。
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